Tight approximation of sums over zeros of L-functions

Abstract: In various contexts explicit formula’s relate sums over primes (eg: numbers or ideals) to sums over zeros of some corresponding L-function(s). The aim of this talk is to explain how we tightly approximate these sums over zeros in the context where one has zero free regions and zero density results for the corresponding L-function(s) and how we use this to get essentially best possible bounds for the error term in the prime number theorem.

This talk discusses joint work with Habiba Kadiri and Joshua Swidinsky as well as ongoing work with Mikko Jaskari and Nizar Bou Ezz.

combinatoricsnumber theory

Audience: researchers in the topic

Lethbridge number theory and combinatorics seminar